A train has a capacity of 154 seats. Tickets for seats are sold at $8 and

Question

$12. There are 1/5 more $8-seats than $12-seats on the train. During a trip the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How
many $8-seats were not taken during the trip?

Answer 1

Let's call the number of $12 seats on the train x. Then we know that there are 1/5 more $8 seats, which means there are 6/5 times as many $8 seats as $12 seats. So the number of $8 seats on the train is 6/5x.

Next, we're told that during the trip, the amount collected from $8 tickets was twice the amount collected from $12 tickets. Let's call the number of $12 tickets sold y. Then the number of $8 tickets sold must be 2y, since the amount collected from $8 tickets was twice as much. We can write an equation based on the total amount collected:

8(2y) + 12y = 540
16y + 12y = 540
28y = 540
y = 19.29

We can't sell a fraction of a ticket, so let's round y down to the nearest whole number, which is 19. That means the number of $12 seats sold was 19, and the number of $8 seats sold was 2(19) = 38.

Now we can figure out how many $8 seats were not taken. We know that the total number of seats on the train is 154, so the number of $12 seats plus the number of $8 seats must equal 154:

x + 6/5x = 154
11/5x = 154
x = 70.909

Again, we can't have a fraction of a seat, so let's round x up to the nearest whole number, which is 71. That means the number of $8 seats on the train is 6/5(71) = 85.2, which we'll round down to 85. We also know that 38 $8 seats were sold, so the number of $8 seats not taken is:

85 - 38 = 47

Therefore, 47 $8-seats were not taken during the trip.